The row about high energy prices has been ignited after British Gas announced its profits had doubled in the first half of this year.
It comes as its parent group Centrica said it would be axing 4,000 jobs, not all of which will be in the UK.
The cut follows a strategic review aimed at delivering savings of £750 million a year by 2020.
British Gas profits were £528 million for the first half of the year, more than it made in the whole of 2014, even though it recently cut prices by 5%.
Which? executive director Richard Lloyd said: "While it's good to see the new commitment from Centrica to focus on serving customers, with British Gas profits high and wholesale prices low, customers will no doubt wonder why cuts to their bills haven't gone further, and haven't included electricity.
"Following the Competition and Markets Authority's blistering assessment of this sector, we expect big suppliers to pass on falling costs to their customers quickly and fairly."
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